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Thread: Need Help with "Exact Values" and absolute value of a linear function.

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    Red face Need Help with "Exact Values" and absolute value of a linear function.

    1. Don't understand how exact values work
    2. |3x-2| = 4 ---- Please solve
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  2. #2
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    Quote Originally Posted by liveboon View Post
    1. Don't understand how exact values work
    2. |3x-2| = 4 ---- Please solve
    (1) If the question asks for the exact value of $\displaystyle \frac{2}{\sqrt{2}}$ , you are expected to give the answer in surd form, $\displaystyle \sqrt{2}$ instead of 1.41 because $\displaystyle \sqrt{2}$ is the more exact value to represent the answer than 1.41

    (2) $\displaystyle 3x-2=\pm 4$
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  3. #3
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    2.
    $\displaystyle |3x - 2| = 4$


    Remember that $\displaystyle |3x - 2| = \begin{cases}\phantom{-(}3x-2\phantom{)}\,\textrm{if }3x - 2 \geq 0\\ -(3x - 2)\,\textrm{if }3x - 2 < 0\end{cases}$

    $\displaystyle = \begin{cases}3x - 2 \,\textrm{if } x \geq \frac{2}{3}\\ 2 - 3x \,\textrm{if }x < \frac{2}{3}\end{cases}$


    So IF $\displaystyle 3x - 2 = 4$ then $\displaystyle x = 2$. Is this possible?

    IF $\displaystyle 2 - 3x = 4$ then $\displaystyle x = -\frac{2}{3}$. Is this possible?
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